Singularly Perturbed Nonlinear Boundary‐Value Problems Whose Reduced Equations Have Singular Points

Abstract

Using results on implicit first‐order differential equations, the existence and the asymptotic behavior of solutions of singularly perturbed second‐order boundary‐value problems whose reduced equations have singular points are studied. The variety of possible nonuniform behavior is investigated by means of a stability analysis of the reduced solutions and is illustrated with several model problems which are canonical in terms of the first‐order singular‐point theory.